what percentage of this effort I charge to the customer.
This almost always 100%, but in some exceptional cases, this may be lower.

In any case I keep all the rights on the generated software while you get a license to use it together with licensed products from me.
( i.e. if you order some enhancement to DemoRecorder 24/7, you can use it with all licenses of DemoRecorder 24/7 in your organisation. )
If such features make sense as part of the product, I include them in the general product and therefore make it available for other customers as well.

I estimate the effort in a unit which I call "engineering unit" which takes into account different skill levels needed for different tasks, and includes possible investments in infrastructure and tools etc needed for a project. ( sometimes, 100 hours of labour can be optimized away by using an appropriate tool which costs significantly less than the saved labour. )
So allows optimal use of resources.
Therefore it is more useful than a man-hour.

As a rule of thumb, one "engineering unit" in terms of labour is about 4 man-hours of a highly skilled engineer.

The current price of an engineering unit is US$ 797

Payment:
Smaller amounts of engineering units are paid with advance payment. ( up to 5 or so. )

mid-sized projects ( up to approx 100 engineering units ) usually payed in three parts as follows:

1/3 advance

1/3 when delivering 50% of the tasks in form of a prerelease

1/3 when everything is finished.

Larger projects are probably payed in more parts, or split it in multiple mid-sized projects.

Hourly payment only as fallback if other schemes do not apply

If, for some work, only hourly payment makes sense, then my hourly rate will be US$199.
( Until now, there never was a necessity for hourly payment in a project connected to DemoRecorder.
But an example may be attending a meeting or a telephone conference.
Or helping you with some of your projects where you need my X11 expertise or other consulting things... )